Both MINE and NWJ suffer from high-variance estimations and to combat such issue, the SMILE estimator was introduced in [1]}. It is defined as
\(I(X;Y) \ge & I_{SMILE}(X;Y) \nonumber \\= & \sup _{\theta \in \Theta } \mathbb {E}_{(\mathbf {x},\mathbf {y})\sim p_{XY}(\mathbf {x},\mathbf {y})}[T_{\theta }(\mathbf {x},\mathbf {y})] \nonumber \\& -\log (\mathbb {E}_{(\mathbf {x},\mathbf {y})\sim p_X(\mathbf {x}) p_Y(\mathbf {y})}[\text{clip}(e^{T_{\theta }(\mathbf {x},\mathbf {y})},e^{-\tau },e^{\tau })]),\) 
